"Daniel L. Lieberman" wrote:

The estimation of a ship's position from the distance run by the log
and the courses steered by the compass, with corrections for current,
leeway, etc., but without astronomical observations. Hence /dead/
latitude (q.v.), that computed by dead reckoning.

The log is the ships log - not a log in the water.

I suspect in this definition, they do mean a log in the water, in the
form of a nautical log, which measured distance by counting knots or
revolutions.

http://91.1911encyclopedia.org/L/LO/LOG.htm